2020-06-04 01:42:57 +00:00
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---
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slug: /silver/binary-search
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2020-06-04 14:28:47 +00:00
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title: "Binary Search"
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2020-06-05 23:04:47 +00:00
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author: Nathan Chen
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2020-06-04 05:39:49 +00:00
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order: 4
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2020-06-05 00:37:02 +00:00
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prerequisites:
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-
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- Silver - Sorting
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2020-06-04 01:42:57 +00:00
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---
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2020-06-05 22:43:24 +00:00
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Binary search can be used on monotonic functions for a logarithmic runtime.
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2020-06-05 22:24:55 +00:00
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2020-06-04 05:39:49 +00:00
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<!-- END DESCRIPTION -->
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2020-06-05 22:43:24 +00:00
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2020-06-05 23:02:56 +00:00
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## The Basic Application
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Find an element in a sorted array in O(log N) time.
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### Tutorial
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2020-06-05 23:04:17 +00:00
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- [GeeksForGeeks](https://www.geeksforgeeks.org/binary-search/)
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- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
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2020-06-05 23:02:56 +00:00
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### Problems
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2020-06-05 23:04:17 +00:00
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- [USACO Silver Counting Haybales](http://www.usaco.org/index.php?page=viewproblem2&cpid=666)
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2020-06-05 23:02:56 +00:00
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## Binary Searching on the Answer
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2020-06-05 23:05:32 +00:00
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Oftentimes used when you need to find the "minimum" or "maximum" of some quantity such that it satisfies some property.
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2020-06-05 23:02:56 +00:00
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### Tutorial
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2020-06-05 23:04:17 +00:00
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- [CPH Section 12.1](https://www.overleaf.com/project/5e73f65cde1d010001224d8a)
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2020-06-05 23:02:56 +00:00
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### Problems
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2020-06-05 23:04:17 +00:00
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- [USACO Silver Cownvention](http://www.usaco.org/index.php?page=viewproblem2&cpid=858)
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- [USACO Silver Cow Dance](http://www.usaco.org/index.php?page=viewproblem2&cpid=690)
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- [USACO Silver Social Distancing](http://www.usaco.org/index.php?page=viewproblem2&cpid=1038)
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- [USACO Silver Loan Repayment](http://www.usaco.org/index.php?page=viewproblem2&cpid=991)
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2020-06-05 23:02:56 +00:00
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- Also needs some math and "sqrt" analysis
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2020-06-05 23:04:17 +00:00
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- [USACO Silver Angry Cows](http://usaco.org/index.php?page=viewproblem2&cpid=594)
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